Analytic solutions to transient groundwater flow under time-dependent sources in a heterogeneous aquifer bounded by fluctuating river stage

• Analytic solutions to transient groundwater flow in a heterogeneous aquifer were derived.
• Heterogeneity increases the spatial variation of h but little effect on lateral discharge.
• The effect of river stage on h and lateral discharge is limited in the zone near the river.

Analytical solutions for the water table and lateral discharge in a heterogeneous unconfined aquifer with time-dependent source and fluctuating river stage were derived and compared with those in an equivalent homogeneous aquifer. The heterogeneous aquifer considered consists of a number of sections of different hydraulic conductivity values. The source term and river stage were assumed to be time-dependent but spatially uniform. The solutions derived is useful in studying various groundwater flow problems in a horizontally heterogeneous aquifer since the spatially piecewise-constant hydraulic conductivity and temporally piecewise-constant recharge and lateral discharge can be used to quantify variations in these processes commonly observed in reality. Applying the solutions derived to an aquifer of three sections of different hydraulic conductivity values shown that (1) the aquifer heterogeneity significantly increases the spatial variation of the water table and thus its gradient but it has little effect on lateral discharge in the case of temporally and spatially uniform recharge, (2) the time-dependent but spatially uniform recharge increases the temporal variation of groundwater table over the entire aquifer but its effect on lateral discharge is limited in the zone near the river, and (3) the effect of river stage fluctuation on the water table and lateral discharge is limited in the zone near the river and the effect of the heterogeneity is to increase lateral discharge to or recharge from the river.